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STEP WISE ASSISTANCE TUTORIAL
DATA ANALYSIS: SECTION IV: SIMULATION OF SERIAL OR CASCADING PERTURBATIONS
The first section of the Main Results Window shown below, allows users to visualize the input network of interest and its various graph based properties.
[The format of this page is the same for both 'Your Web' and 'Browse Webs' sections of NEXCADE.]
As seen above, the fourth and last section allows users to simulate complete cascades of perturbation on the system of interest.
Users can choose between two opposite sequences of node-removals to carry out the serial extinctions, based on degree.
The option 'Highest To Lowest' simulates the removal of every node from the network beginning with the node that has the highest connectivity, while the option 'Lowest To Highest' simulates sequential removal of nodes from the network in the exact reverse order.
On clicking the 'RUN CASCADE' button for the Yeast RNA-protein example network in the 'Highest to Lowest' mode, the following page is returned.
As can be seen above, NEXCADE informs the user about the number of nodes whose removal results in complete network collapse. Users can monitor the status of the initial network at each step of the perturbation, or get an overview of the change in critical network attributes during the perturbation, and finally download the raw data of the simulation for further analyses.
A similar page is returned on clicking the 'RUN CASCADE' button for the Yeast RNA-protein example network in the opposing order, i.e 'Lowest to Highest' mode:
Note the contrast between the two figures above even though they appear similar at first sight.
In case of the 'Highest To Lowest' perturbation sequence, the YPRN network collapses completely when only 40 out of over 460 total nodes are perturbed. However, when nodes ar removed in the opposing order, the network is able to tolerate the removal of almost 430 nodes without undergoing system collapse.
PART I : VISUALIZATION & ANALYSIS
As mentioned above, users can monitor the system and visualize / analyse details of the reduced subnetworks at each step of the sequential perturbation, as shown below.
As shown above, one can get a birds eye overview of the effect of each of the 40 removals on the network. For example, the first node removal in this cascade is associated with 313 secondary extinctions, causing a drastic reduction in network size from 462 to 148 nodes.
The name of the perturbed node is depicted in the 5th column followed by a link that enables more detailed analysis of the remaining sub-network at this stage.
Clicking the 'Analyse Subnetwork' link against the first node removal returns the following:
A Table as shown above allows users to compare critical network attributes between the initial unperturbed network (Row 1) with the reduced web at the stage of interest (Row 2).
For example, It is clear that the first primary removal (Col 8) causes 313 secondary removals (Col 9) resulting in a drastic reduction in network size and interactions (Col 2 and 3). This single perturbation further increases the number of disconnected network compartments to 21 from initial 19 (Col 4).
The change in the average network degree, path length and density can be observed in Cols 5 - 7.
In contrast to the above outcome, the first subnetwork of the cascade when the opposing extinction sequence is simulated, gives the follwoing outcome:
Note that when the node with the lowest connectivity is removed, this primary removal (Col 8) causes no substantial secondary effects on any other network property, as shown on the comparative table above.
Clicking on the appropriate link in the second panel of either of the above two figures, enables visualisation of the sub-network as shown below.
The figure shows the resulting subnetwork after the first primary removal in the 'Highest To Lowest' cascade resulting in a drastic reduction in network size and interactions and an increase in number of disconnected network compartments to 21.
Users can use this page to view various node attributes of each remaining node in the subnetwork as explained in earlier tutorials, as well as to obtain a high resoution image of the network.
By clicking the appropriate linkis in the second panel of the 'Analyse Sub-network' Page shown earlier, users can get a list of the interactions as well as secondary extinctions, if any, resulting after the respective perturbation.
As shown above, the list of remaining interactions in the sub-network at the stage of interest can be used as input to NEXCADE in order to study any network-specific aspects designed by interested users. This list can also be used as input to various other network analysis programs avaialble online for other kinds of analyses.
PART II : GRAPHICAL VIEW OF NETWORK RESPONSE TO PERTURBATION
As mentioned above, users can get an overview of the change in critical network attributes during the perturbation cascade, in a graphical manner.
For example, one can visualise how the initial network size decreases with each perturbation in the series, as a function of the percentage nodes removed. One can also monitor the effect on overall interactions, secondary extinctions as well as total extinctions, i.e the combined number of primary and secondary removals at each stage of the perturbation, as shown below:
As shown above, when the nodes are removed in an ordered manner starting with the most highly connected node, the network collapsesi (i.e its size becomes zero) in less than 10% removals. This response is in sharp contrast with the robust response shown by the same network to the opposing sequence of perturbation, as shown below:
Note that when the nodes are removed from 'Lowest To Highest' degree (RED) , the network remains stable for more than 90% removals, as compared to less than 10% when the most connected nodes are removed first (GREEN).
This figure shows the contrasting response of the network in terms of change in secondary extinctions between the two cascades.
PART III: DOWNLOAD RAW DATA
For each extinction cascade sequence, users can also download or view the raw results of the extinction simulation data at every stage of the perturbation sequence, as shown below:
As shown above, the data is divded into eight columns for convenience.
This completes the last section of network analysis tutorial.
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